Graphs of Proportional Relationships Quick Check
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Question
Use the image to answer the question.
A graph with x-axis and y-axis ranging from 0 to 8 in unit increments shows a line. The line passes through the following plotted points: left parenthesis 0 comma 0 right parenthesis; left parenthesis 2 comma 3 right parenthesis; and left parenthesis 4 comma 6 right parenthesis.
Identify the constant of proportionality from the graph.
(1 point)
Responses
2
2
23
Start Fraction 2 over 3 End Fraction
12
Start Fraction 1 over 2 End Fraction
32
The correct answer is 2.
To identify the constant of proportionality from the graph, we need to find the ratio of the y-values to the x-values for any two points on the line.
Let's choose two points: (0, 0) and (2, 3).
The ratio of the y-values to the x-values is: 3/2.
Therefore, the constant of proportionality is 3/2.
So, the correct answer is 23, which is Start Fraction 2 over 3 End Fraction.
To identify the constant of proportionality from the graph, we need to look at the relationship between the x-values and the y-values of the plotted points.
In this case, the graph passes through the points (0, 0), (2, 3), and (4, 6).
To find the constant of proportionality, we can calculate the ratio of the change in y-values (Δy) to the change in x-values (Δx) between any two points.
Let's take the points (0, 0) and (2, 3) to calculate this ratio:
Δy = 3 - 0 = 3
Δx = 2 - 0 = 2
The ratio Δy/Δx is 3/2, which simplifies to 1.5.
Therefore, the constant of proportionality from the graph is 1.5.
So, the correct response is:
Start Fraction 2 over 3 End Fraction